Nuclear fission
-Fission: what is it?
-The main steps toward nuclear
energy
-How does fission work?
-Chain reactions
What is nuclear fission?
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Nuclear fission is when a
nucleus break into two or
more nuclei.
This process yields a net
energy gain when the initial
nucleus is heavy enough.
•Consider the possibility that A ÆA1+A2. The mass of A is given by:
M(A)c2 =(Z1+Z2)mpc2 + (N1+N2)mnc2 -Eb(A)
The binding energy of A, Eb(A), for large A, is:
Eb(A)=A ε(A)= A1 ε(A) + A2 ε(A)< A1 ε(A1) + A2 ε(A2) Î
M(A)c2 > M(A1)c2+ M(A2)c2
•In this case the reaction can occur spontaneously.
•When moving from U to A about 100, the energy gain per nucleon is
about1 MeV, so the typical energy gain from a U fission is about 200 MeV.
A little of history
1934 Ida Noddack mentions fission as an hypothesis for the non existence of long
lived nuclei beyond Z=92
1934 Fermi group produce nuclear transmutations by neutron bombardment, by
means of (n,γ) and n(α) reactions. When U was bombarded, they obtained
fission, but misinterpreted it.
1938 Hahn and Strassman bombarded U and discovered Ba in the reaction
products. Lise Meitner ( a former assistant of Hahn, flown to Sweden for
escaping the racial laws of nazist Germany) ) and his nephew explain the
experimental result as due to fission. In 1944 Hahn got the Nobel Prise
(
)Joliot-Curie's team in Paris discovered that secondary neutrons are released
during uranium fission, thus making a nuclear chain-reaction feasible
1942 Fermi and Szilard created the first man made reactor, Chicago Pile 1
1945 The first “atomic” (fission) bomb was exploded in Alamogordo, and soon
later in Hiroshima and Nagasaki
1951 Electricity was generated form a nuclear reactor (100 kW ) at Arco, Idaho
1954 USSR's Obninsk Nuclear Power Plant became the world's first nuclear power
plant to generate electricity for a power grid, and produced around 5
megawatts of electric power.
1957 First nuclear powered submarine…
History of the
Global Nuclear
Power Industry
• All utility-scale reactors
heat water to produce
steam, which is then
converted into
mechanical work for the
purpose of generating
electricity or propulsion.
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In 2007, 14% of the world's electricity came from nuclear power, from
some 440 nuclear reactors.
Nuclear power accounts for 77% of electricity in France, 34.5% in
Japan, 26% in Germany and 19% in US.
More than 150 nuclear-powered naval vessels have been built, and a
few radioisotope rockets have been produced.
Spontaneous Fission
• As discovered by Flyorov and
Petrhak in 1940, Uranium nuclei,
beside the dominant alpha decay mode,
can also have spontaneous fission,
into two fragments with A around 100.
•In the liquid drop model, comparison between surface energy (Es =as
A2/3) and Coulomb energy (Ec =ac Z2/A1/3 ) shows that nuclei are
unstable to fission for Z2/A>18, i.e for nuclei heavier than 90Zr.
•The Liquid Drop model can be used to estimate the energy release in
fission. For 235U it is about 200 MeV per nucleus and it mostly comes
from the coulomb energy. The energy released is approximately divided
up as follows: Fragment kinetic energies 165 MeV, Prompt Neutrons 5
MeV Prompt gammas 7MeV, Radioactive decay fragments 25 MeV
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Nuclide Half-life
Fission prob.
per decay (%)
Neutrons per fission
235U
7.04x108 years 7.0x10-9 %
1.86
238U
4.47x109 years 5.4x10-5 %
2.07
Spontaneous “Fission lifetimes”*
• They range from 1016 yr for 238U to 10-2
yr for 256Fm.
•Very much like for alpha decay, the
process of fission is suppressed by the
presence of a potential barrier.
•The figure below shows schematically
the shape of the barrier as a function of
the deformation or fragment separation
for different values of the atomic mass
number, A.
•Consider 238U Î 145La+90Br+3n, the
fission rate is 3 1024 s to be compared
with decay rate of 5 1018 s-1. i.e the fission
probability is 0.5 10-6. This since heavy
particles have to tunnel thorugh a barrier.
•Alpha decay is a limiting case of fission
*They are defined as inverse of the fission
decay rate
Neutrons from Spontaneous
Fission
• We have already seen that in 238U Î
145La+90Br+3n three neutrons are emitted.
•There are several channels for 238U
spontaneous fission, with an average
neutron number of 2.07
•Neutron emission is a general feature of
(spontaneous and induced) fission.
•At large A one has N>>Z, in order to
diminisish Coulom repulsion, whereas at
low and intermediate A the stable nuclei
have Z ≈N.
•So there is generally an excess of
neutrons, which have to be emitted.
Nuclide Half-life
Fission prob.
per decay (%)
Neutrons per fission
235U
7.04x108 years 7.0x10-9 %
1.86
238U
4.47x109 years 5.4x10-5 %
2.07
Induced Fission
• For inducing fission, one has to provide energy to
the nucleus, so that its parts can overcome the
fission barrier, or form a compound nucleus where
the barrier is diminished or eliminated.
•In principle on can induce fission by :
-photofission
γ+ (Z,A) Î (Z,A)* Î (Z1,A1) + (Z2,A2) +neutrons
-proton induced fission
p+ (Z,A) Îp+ (Z,A)* Î (Z1,A1) + (Z2,A2)+neutrons
-neutron induced fission
n+ (Z,A) Î (Z,A+1)* Î (Z1,A1) + (Z2,A2)+neutrons
Nuclide Half-life
Fission prob.
per decay (%)
Neutrons per fission
235U
7.04x108 years 7.0x10-9 %
1.86
238U
4.47x109 years 5.4x10-5 %
2.07
Neutron Induced
Fission
• Neutron induced fission,
n+ (Z,A) Î (Z,A+1)* Î (Z1,A1)
+ n’s
is particularly effective for the
following reasons:
1)neutrons are penetrating,
2)slow neutrons cross sections
are large, order 100-1000 barn
at thermal energies (see later)
3) Neutrons are regenerated
during fission
The induction of fission by
neutron absorption and the
susequent emission of neutrons
in the process of fission leads to
the possibility of a self
sustaining or chain reaction.
Fission fragments
and fission
products
•Fission fragments have a
double bell distribution as a
function of A.
•Note that they are unstable,
as are neutron rich they
decay towards stable nuclei
by a chain of beta decays.
•This yields the so called
“fission products”
•Some fifty per cent of fission
products have decay times
less than one year, the rest
has lifetimes that can be as
long as million years,
Neutrons from
Fission
• One distinguishes two types
of
neutrons from fission:
-prompt neutrons,
They are those accompanying
the two nuclear fragments,
e.g, the 2n in 235U+nÆ 93Rb +141Cs+2n
In the case of 235U , there are on the average 2.42 prompt neutrons
-delayed neutrons
These are associated with the beta decay of the fission products. Indeed,
after prompt fission neutron emission the residual fragments are still neutron
rich. They undergo a β decay chain. In some cases the available energy in
the β decay is high enough for leaving the residual nucleus in such a highly
excited state that neutron emission instead of gamma emission occurs.
(beta delayed neutron emission)
Delayed neutrons have delays of order seconds. They are about 1/100
fissions. Delayed neutrons are essential for the control of nuclear reactors
The fate of neutrons in
Uranium (I)
• Natural uranium is an admixture
of 235U (presently 0.7%) and 238U
•Neutrons emerging from fission
have an energy spectrum peaked
at about 1 MeV.
•Neutrons in Uranium can have
several processes:
-Elastic (n,n) and inelastic
scattering (n.n’)
-Neutron capture (n,γ)
-Fission (n,f)
•Elastic and inelastic scattering
have the effect of slowing down
neutrons
•Neutron capture removes neutron
frome the chain
•Only fission can reproduce
neutrons
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The fate of neutrons in
Uranium (II)
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235U
will fission (n,f) at all energies of
the absorbed neutron. It is a FISSILE
material
Note the 1/v behaviour of fission corss
section at low velocities, typical of
esothermal processes.
235U fission cross section can grow
very large, to 500 barns at thermal
energies
238U has a threshold for fission (n,f) at
a neutron energy of 1MeV. This
effectively prevents fission from
occurring in 238 U
There is very strong reasonant
capture of neutrons (n, γ) for energies
in the range 10-100 eV - particularly in
the case of 238U where the crosssection reaches very high values.
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